790 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 6, NO. 6, DECEMBER 2017
Quadrature Channel Modulation
Ibrahim Yildirim, Student Member, IEEE, Ertugrul Basar, Senior Member, IEEE, and Ibrahim Altunbas, Member, IEEE
Abstract—In this letter, we propose the concept of quadrature channel modulation (QCM) by combining quadrature spatial modulation (QSM) and media-based modulation (MBM) trans- mission principles. The proposed QCM schemes exploit not only the in-phase and quadrature components of complex data symbols for antenna indexing but also channel states for the transmission of additional information bits through index mod- ulation by employing a single radio frequency (RF) chain. It is shown via numerical studies that the proposed QCM schemes can outperform the existing emerging schemes such as QSM, plain MBM, and spatial modulation-based MBM, which also employ a single RF chain at their transmitters.
Index Terms—Channel modulation, index modulation, media- based modulation, quadrature spatial modulation.
I. INTRODUCTION
INDEX modulation (IM) provides new dimensions for the transmission of digital information and can be implemented by considering the indices of the transmit antennas (TAs) of a multiple-input multiple-output (MIMO) system [1], the subcarriers of an orthogonal frequency division multiplexing system [2] or the radio frequency (RF) mirrors of a reconfig- urable antenna (RA) [3]. An RF mirror is an RA element that contains a PIN diode, which can be turned on or off according to the information bits to alter the radiation pattern of an RA [4], [5]. Some initial studies have been also per- formed for the practical realization of RAs with RF mirrors. As an example, Ourir et al. [6] implemented a compact RA with two RF mirrors and showed the corresponding radiation patterns, each of which leads to a different fading chan- nel realization. Due to their attractive advantages such as improved energy/spectral efficiency, better error performance and lower complexity detection, over traditional digital mod- ulation schemes [7], IM techniques have attracted remarkable attention in the past few years [8].
Although RAs with parasitic elements that are capable of altering their radiation patterns, are well-known in the field of electromagnetics; the concept of media-based mod- ulation (MBM), which is one of the newest members of the vast IM family, has been proposed explicitly for the utiliza- tion of RAs to carry digital information [3], [9]. To resolve this ambiguity, the more general term of channel modula- tion (CM) has been recently introduced in [10] for the family of MBM/RA systems, which are actually based on the same
Manuscript received July 28, 2017; accepted August 17, 2017. Date of publication August 22, 2017; date of current version December 15, 2017. The associate editor coordinating the review of this paper and approving it for publication was V. Raghavan. (Corresponding author: Ertugrul Basar.)
The authors are with the Faculty of Electrical and Electronics Engineering, Istanbul Technical University, 34469 Istanbul, Turkey (e-mail: yildirimib@itu.edu.tr; basarer@itu.edu.tr; ibraltunbas@itu.edu.tr).
concepts. In both systems (also in space-shift keying (SSK) that considers transmit antenna indices for IM), a carrier signal with constant parameters is transmitted while the realizations of the wireless channel convey information, i.e., the modu- lation of the wireless channel itself is performed from the perspective of the receiver. It has been also proved in [10] that MBM and SSK schemes are identical for specific system parameters.
The recent study of [11] considered the combination of gen- eralized SM (GSM) techniques with MBM. It has been shown that due to additional information bits transmitted by antenna indices, GSM-MBM can achieve a better error performance than MIMO-MBM. A dual-polarized SM scheme, which con- siders the dimension of polarization for the transmission of an additional one information bit, is proposed in [12] for cor- related Rayleigh and Rician fading channels. More recently, multidimensional IM concept is introduced in [13], where both RF mirrors, transmit antennas and time slots are con- sidered for IM. SSK and MBM principles are also combined in [4] to improve the error performance of SSK consider- ing correlated and nonidentically distributed Rician fading channels. Later, RA-based SSK [4] is considered for under- lay cognitive radio systems in Rician fading channels and improvements are shown compared to conventional spectrum sharing systems [5]. Finally, the scheme space-time chan- nel modulation (STCM) is introduced in [10] by combining space-time block coding and MBM concepts to further obtain transmit diversity gains. However, the design of high data rate SM-based CM schemes with single RF chain is still waiting to be explored.
In this letter, we introduce the concept of quadrature chan- nel modulation (QCM) by combining quadrature SM (QSM) and MBM transmission principles to further improve the data rate of SM/SSK-based MBM (RA) schemes while ensuring simple implementation with a single RF chain. QSM appears as a promising SM variant with its high spectral efficiency and simple transceiver structure [14]. Our aim is to bring the attractive advantages of QSM, such as improved spectral effi- ciency and simple transceiver structure, into the field of CM by carefully designing a joint transmission mechanism, which outperforms both QSM and MBM schemes in terms of spec- tral efficiency and BER performance. Inspired by QSM, our scheme has three different operation modes that can provide interesting trade-offs among BER performance, data rate and complexity. Furthermore, our scheme can provide the same spectral efficiency as that of QSM by exploiting a considerably lower number of transmit antennas and only a single RF chain. It has been shown by theoretical average bit error rate (BER) derivations as well as comprehensive numerical studies that the proposed schemes can achieve better error performance than the reference single-input multiple-output (SIMO)-MBM, SM-MBM and conventional QSM schemes.
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YILDIRIM et al.: QCM 791
Fig. 1. Block diagram of the QCM-I/II schemes for an Nr × Nt MIMO system (The terms in parentheses are valid for the QCM-II scheme).
II. QUADRATURE CHANNEL MODULATION
In this section, we introduce the concept of QCM as well as provide design examples. Three novel QCM schemes are proposed by considering a MIMO system with Nr receive and Nt transmit antennas that employs Q-ary quadrature ampli- tude modulation (Q-QAM). Furthermore, each TA is equipped with M RF mirrors, which are used to create different channel realizations according to the information bits.
i) QCM-I Scheme: The system model of the QCM-I scheme is shown in Fig. 1. As seen from Fig. 1, this scheme is obtained by the direct combination of QSM and MBM principles. A total of
η = log2(Q) + 2log2(Nt) + M (1)
bits enter the transmitter of the QCM-I scheme per channel use. Similar to the QSM scheme, the first log2(Q) bits of the incoming bit sequence are used for ordinary Q-QAM, while the subsequent 2log2(Nt) bits select the indices (lR and lI) of TAs for the transmission of in-phase and quadrature compo- nents of the selected Q-QAM symbol x. However, the last M bits are reserved for the selection of the active channel state (k), which is the same for all possible activated TAs of the QCM-I scheme. In other words, the QCM-I scheme extends the ordinary QSM into a third dimension, which is the dimen- sion of channel states, to transmit additional information bits. In the following, we give an example for the operation of the QCM-I scheme.
Example 1: We consider the following system parameters: Nt =Nr =4,Q=16,M=2andη=10bitsperchannel use (bpcu). Assume that the input bits are grouped as follows:
q=[1001 11 10 01]. (2)
log2 (Q) log2 (Nt ) log2 (Nt ) M
The first log2(Q) = 4 bits (1 0 0 1) are modulated to
obtain the 16-QAM symbol x = 3 + j. This data symbol is
mirrors for both activated TAs: 1st RF mirror → off and 2nd RF mirror → on.
ii) QCM-II Scheme: This scheme is proposed to further improve the spectral efficiency of the QCM-I scheme by ensur- ing that the real and imaginary components of the complex data symbols are not only transmitted from different TAs but also with two independent channel state realizations, which doubles the number of RF mirror bits. In order to perform two independent channel state selections (kR and kI) for the QCM-II scheme, first, the set of available TAs is split in half into two groups and an antenna index lR is selected for xR from all available TAs without considering these groups. However, to activate a different antenna and perform a second chan- nel state selection for xI, the group associated with lR is not considered for lI. The reason for this adaptive selection is to transmit more number of IM bits via TA indices as seen from Fig. 1. As a result, the spectral efficiency of the QCM-II scheme becomes
η = log2(Q) + log2(Nt) + log2(Nt/2) + 2M bpcu. (3)
iii) QCM-III Scheme: This QCM scheme is inspired from the QCM-I scheme; however, it owns a reserved TA as in [15], which is employed instead of the selected TA of xR to inde- pendently perform active channel state selection for xR and xI, similar to the QCM-II scheme. On the other hand, due to the utilization of a reserved TA, there is no need for TA partitioning as in the QCM-II scheme, and a higher spectral efficiency can be obtained by considering two parallel virtual SM-MBM schemes for both xR and xI as shown in Fig. 2. Consequently, the spectral efficiency of this scheme becomes
η = log2(Q) + 2log2(Nt) + 2M bpcu. (4)
Example 2: We consider the following system parameters: Nt =4,areservedTA,Nr =4,Q=4,M=2andη=10 bpcu. Assume that the input bits are grouped as follows:
q=[11 10 10 0111]. (5)
log2(Q) log2(Nt) log2(Nt) M M
The first log2(Q) = 2 bits ( 1 1 ) are modulated to obtain
the 4-QAM symbol x = 1 − j, which is decomposed into its
real and imaginary components as xR = 1 and xI = −1.
Then, the subsequent log2(Nt) = 2 bits ( 1 0 ) determine the antenna index lR = 3 over which the real component xR will be transmitted. For xI, the reserved TA is employed
partitioned into its real and imaginary components as xR = +3
and xI = +1. Then, the next log2(Nt) = 2 bits (1 1) deter-
mine the antenna index lR = 4 over which the real component
xR will be transmitted. Similarly, the following log2 (Nt ) = 2
bits ( 1 0 ) select the antenna index lI = 3 over which the imaginary component xI will be transmitted. Finally, the last M bits select the second channel state (k = 2), which cor- responds to the following on/off status of the available RF
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792 IEEE WIRELESS COMMUNICATIONS LETTERS, VOL. 6, NO. 6, DECEMBER 2017
Fig. 2. Block Diagram of the QCM-III scheme for an Nr × (Nt + 1) MIMO system.
instead of the previously selected TA for xR, and the next
log2(Nt) = 2 bits ( 1 0 ) select lI = 4 from the available TA set {1,2,4,5} since the third antenna has already reserved. Finally, the remaining 2M = 4 bits can select two indepen- dent channel states, which are kR = 2 and kI = 4, for the two activated TAs lR = 3 and lI = 4, respectively.
The baseband signal model of the QCM scheme can be expressed as
y = Hs + n (6)
where y ∈ CNr×1 and n ∈ CNr×1 are vectors of the received signals and noise samples, respectively. H and s respectively stand for the extended channel matrix and transmission vector of the QCM scheme. For QCM-I/II schemes, their dimensions are Nr ×2M Nt and 2M Nt ×1, respectively, while the correspond- ing dimensions for the QCM-III scheme are Nr × 2M (Nt + 1) and 2M (Nt + 1) × 1. We assume that the elements of H and n follow CN (0, 1) and CN (0, N0) distributions, respectively. The general form of s is given as
The maximum-likelihood (ML) detection for QCM schemes can be performed by the following exhaustive search:
[xˆ, ˆlR, ˆlI, kˆR, kˆI] = arg min ∥y − Hs∥2 (9) x,lR ,lI ,kR ,kI
where ∥.∥ stands for the Euclidean norm.
III. THEORETICAL ANALYSIS OF QCM
In this section, theoretical average BER of QCM is evalu- ated considering the system model of (6). If s is transmitted anditiserroneouslydetectedassˆ,thecorrespondingcondi- tional pairwise error probability (PEP) is given by [10]
←−→
←−−−−−−→
←−→
←−→
e(s, sˆ) stands for the number of bit errors for the pairwise error event of (s → sˆ).
IV. NUMERICAL STUDIES
In this section, we provide computer simulation results for the proposed QCM schemes and make comparisons with the classical QSM [14], SIMO-MBM [3] and SM-MBM [11] schemes with respect to Eb/N0, where Eb is the average trans- mitted energy per bit. We consider natural mapping for channel states and TA indices, while we employ Gray mapping for M-PSK/QAM symbols.
In Fig. 3, the theoretical average BER upper bounds of the QCM-I scheme are compared with computer simulation results for different spectral efficiency values, while similar results can be easily obtained for the QCM-II/III schemes. As seen from Fig. 3, the derived theoretical average BER
Ch. State 1
Ch. State 2
lR
Ch. State 3
Ch. State 4
lI
T
s=[00000¦00 1 00¦00000¦000−j0]. ←−−−→ ←−−−−−→ ←−−−→ ←−−−−−→
Ch. State 1 Ch. State 2 Ch. State 3
Ch. State 4
(8)
Similarly, the transmission vector for the QCM-II scheme can be easily obtained.
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P(s → sˆ|H)=P(∥y−Hs∥2 >y − Hsˆ2) = Q
2N0
2
where = ∥H(s − sˆ)∥ . Using the alternative form of the
Q-function and moment generating function [16] of , given by M(t) = (1 − t∥s − sˆ∥2)−Nr , the unconditional PEP is obtained as
lRlI ⎛⎞N π r
s=[··· ¦0···xR ···0¦··· ¦0···jxI···0¦··· ]T ←−−−−−−−−→ ←−−−−−−−→
Ch. State kR Ch. State kI
(7)
where for the QCM-I scheme, kR = kI = k, while kR and kI are independently selected for QCM-II/III schemes. It should be noted that only one or two elements of s are non-zero. Furthermore, QCM-II/III schemes also ensure that lR ̸= lI to enable independent channel state selections for xR and xI. For the above two examples, the corresponding transmission vectors are respectively given as follows:
lI lR
T
s=[0000 ¦00 j 3 ¦ 0000 ¦ 0000],
1 2 ⎜ sin2θ ⎟
P(s→sˆ)= ⎝ 2⎠dθ (11)
which has a closed form solution in [16]. After the derivation
π0 sin2θ+∥s−sˆ∥ 4N0
of unconditional PEP, the average BER upper bound of QCM
can be obtained with P ≈ 1 P(s → sˆ)e(s,sˆ), where b η2η s sˆ
(10)
YILDIRIM et al.: QCM
793
Fig. 3.
and receive antennas and two RF mirrors with different bpcu values.
(I-CSI) case, the channel matrix at the receiver is obtained as Hˆ = H + E, where the elements of E follow CN (0, σε2) distribution. It is assumed that the power of channel estimation errors is related with N0 as ψ = N0/σε2. As seen from Fig. 4, the proposed schemes are also robust to channel estimation errors as the reference systems for ψ = 1.
V. CONCLUSION
In this letter, we have proposed the concept of QCM to improve the data rate of plain MBM and QSM schemes by exploiting both channel states and in-phase/quadrature com- ponents of the complex data symbols for data transmission through IM. We have shown by extensive numerical studies and theoretical derivations that the proposed QCM schemes with single RF chain outperform the classical QSM and existing MBM-based systems. The design of low-complexity detectors for the proposed QCM schemes, due to the spar- sity of their transmission vectors, can be considered as our future work.
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Theoretical average BER of the QCM-I scheme with four transmit
Fig. 4.
and receive antennas, two RF mirrors and η = 12, (I-CSI: imperfect CSI).
BER performance of QCM and reference systems with four transmit
upper bounds accurately predict the BER performance of the proposed scheme.
In Fig. 4, we provide BER performance curves of the proposed QCM schemes and make comparisons with the ref- erence systems for η = 12 bpcu. As seen from Fig. 4, all three proposed QCM schemes achieve considerably bet- ter BER performance than the reference QSM, SIMO-MBM and SM-MBM schemes, which also employ a single RF chain at their transmitters. The reason for this BER performance improvement can be explained by the fact that the reference MBM and QSM schemes need to employ higher order constel- lations to reach the same spectral efficiency as that of QCM schemes. Similarly, the proposed schemes can achieve a higher spectral efficiency than the reference systems for the same modulation order since the proposed schemes employ a more effective IM mechanism. It is interesting to note that QCM-III scheme achieves the best BER performance by using an addi- tional reserved TA. On the other hand, the QCM-II scheme provides a satisfactory BER performance and outperforms the QCM-I scheme with a more complicated mapping rule. In Fig. 4, we also investigate the performance of the proposed as well as reference systems in the presence of channel esti- mation errors. For the imperfect channel state information
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